
Fermat's Last Theorem
Basic Tools
Takeshi Saito(Author)
American Mathematical Society (Publisher)
Published on 30. December 2013
Book
Paperback/Softback
200 pages
978-0-8218-9848-2 (ISBN)
Description
This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics. Crucial arguments, including the so-called $3$-$5$ trick, $R=T$ theorem, etc., are explained in depth. The proof relies on basic background materials in number theory and arithmetic geometry, such as elliptic curves, modular forms, Galois representations, deformation rings, modular curves over the integer rings, Galois cohomology, etc. The first four topics are crucial for the proof of Fermat's Last Theorem; they are also very important as tools in studying various other problems in modern algebraic number theory. The remaining topics will be treated in the second book to be published in the same series in 2014. In order to facilitate understanding the intricate proof, an outline of the whole argument is described in the first preliminary chapter, and more details are summarised in later chapters.
Reviews / Votes
The book ... is very clear and thorough, and may be recommended to anyone interested in understanding one of the deepest results of the twentieth century in mathematics." - Zentralblatt fur MathematikMore details
Series
Language
English
Place of publication
Providence
United States
Weight
260 gr
ISBN-13
978-0-8218-9848-2 (9780821898482)
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Schweitzer Classification
Person
Takeshi Saito, University of Tokyo, Japan